Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain  interest rate

Lin Xu; Rongming Wang

doi:10.3934/jimo.2006.2.165

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2006, Volume 2, Issue 2: 165-175. Doi: 10.3934/jimo.2006.2.165

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Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate

Lin Xu¹ and
Rongming Wang^1,

1.
Department of Statistics, East China Normal University, Shanghai 200062, P.R.

Received: October 31, 2005

Revised: December 31, 2005

Published: March 2006

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Abstract

In this paper, ruin probabilities are examined in a discrete time risk model in which the interest rates follow a Markov chain with a denumerable state space and the net losses(the claim amount minus the premium income) are assumed to have a dependent AR(1) structure. An upper bound for ultimate ruin probability is obtained by martingale approach. Recursive equations for both finite time ruin probabilities and ultimate ruin probability are derived. By integrating the inductive method and the recursive equation, an upper bound is given for both finite time ruin probabilities and ultimate ruin probability.

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Mathematics Subject Classification: 60K05, 62P05, 90A46.

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